Spatiotemporal symmetry and multifractal structure of head movements during dyadic conversation.

This study examined the influence of sex, social dominance, and context on motion-tracked head movements during dyadic conversations. Windowed cross-correlation analyses found high peak correlation between conversants’ head movements over short (≈2-s) intervals and a high degree of nonstationarity. Nonstationarity in head movements was found to be positively related to the number of men in a conversation. Surrogate data analysis offsetting the conversants’ time series by a large lag was unable to reject the null hypothesis that the observed high peak correlations were unrelated to short-term coordination between conversants. One way that high peak correlations could be observed when 2 time series are offset by a large time lag is for each time series to exhibit self-similarity over a range of scales. Multifractal analysis found small-scale fluctuations to be persistent, τ(q) 0.5. These results are consistent with a view that symmetry is formed between conversants over short intervals and that this symmetry is broken at longer, irregular intervals. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

一种时间序列多重分形分析的改进方法及其应用

通过分析时间序列广义维数的不同计算方法,本文引入一种新的多重分形奇异测度概念,提出了一种时间序列多重分形分析的改进方法。该方法不仅计算量小,而且其得到的连续分段线性曲线序列的广义维数具有恒等于１ 的性质。由于现实中许多信号可以用连续分段线性曲线逼近,因此上述性质深入刻划了这类信号的一个共同特征。仿真结果表明,本文推导出的性质为信号奇异性检测开辟了一条新途径,利用本文方法还可以快速有效地提取实测舰船噪声的短时多重分维特征。     

An Airborne Radar Clutter Tracking Algorithm Based on Multifractal and Fuzzy C-Mean Cluster

For an airborne Iookdown radar, clutter power often changes dynamically about 80 dB with wide distributions as the platform moves. Therefore, clutter tracking techniques are required to guide the selection of const false alarm rate （CFAR） schemes. In this work, clutter tracking is done in image domain and an algorithm combining multifractal and fuzzy C-mean （FCM） cluster is proposed. The clutter with large dynamic distributions in power density is converted to steady distributions of multifractal exponents by the multifractal transformation with the optimum moment. Then, later, the main lobe and side lobe are tracked from the multifractal exponents by FCM clustering method.     

Multifractal signatures of infectious diseases

Incidence of infection time-series data for the childhood diseases measles, chicken pox, rubella and whooping cough are described in the language of multifractals. We explore the potential of using the wavelet transform maximum modulus (WTMM) method to characterize the multiscale structure of the observed time series and of simulated data generated by the stochastic susceptible-exposed-infectious-recovered (SEIR) epidemic model. The singularity spectra of the observed time series suggest that each disease is characterized by a unique multifractal signature, which distinguishes that particular disease from the others. The wavelet scaling functions confirm that the time series of measles, rubella and whooping cough are clearly multifractal, while chicken pox has a more monofractal structure in time. The stochastic SEIR epidemic model is unable to reproduce the qualitative singularity structure of the reported incidence data: it is too smooth and does not appear to have a multifractal singularity structure. The precise reasons for the failure of the SEIR epidemic model to reproduce the correct multiscale structure of the reported incidence data remain unclear.     

Multifractal analysis of Mg-doped ZnO thin films deposited by sol–gel spin coating method

A multifractal analysis has been performed on the 3D (three-dimensional) surface microtexture of magnesium-doped zinc oxide (ZnO:Mg) thin films with doping concentration of 0, 2, 4, and 5%. Thin films were deposited onto the glass substrates via the sol–gel spin coating method. The effect of magnesium doping, on the crystal structure, morphology, and band gap for ZnO:Mg thin films has been analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM), atomic force microscopy (AFM), and UV–Vis spectroscopy. It has been observed that the surface of ZnO thin films is multifractal in nature. However, multifractality and complexity observed to decrease with increasing content of Mg in ZnO thin films due to formation of islands on the surface in accordance with Volmer–Weber growth mechanism. The investigations revealed that crystallinity, microtexture, morphology, and optical properties of the thin films can be tuned by controlling the Mg content within the ZnO lattice. In particular, their optical band gap energies were 3.27, 3.31, 3.34, and 3.33 eV at 0, 2, 4, and 5%, respectively. The prepared thin films of ZnO:Mg with tuned characteristics would have promising applications in optoelectronic devices.     

齿轮故障信号多重分形维数的形态学计算方法

针对传统的多重分形维数计算方法的缺陷,提出基于数学形态学操作的多重分形维数计算方法,并证明了与盒计数法计算多重分形维数的一致性.对实际的齿轮正常、齿面磨损故障和断齿故障信号进行了分析,结果表明,与盒计数法相比,基于数学形态学计算的多重分形维数能够准确区分齿轮的工作状态,并且数学形态学只涉及简单的加减和取大、取小运算,计算更加简单、快速.     

基于小波的多重分形图像去噪新算法

针对多重分形分析很难估计有限长离散数据的多重分形谱这一问题,提出了一种基于奇异性分析的多重分形图像去噪算法.通过定义基于小波系数矩的配分函数,给出了一种有限长离散数据序列多重分形谱估计方法.图像去噪算法中图像的性质由多重分形谱决定,对噪声的类型没有提出任何假设条件,而是通过定义一个基于二维微局域(2-mi-crolocal)分析的变换算子对每一点的Hausdorff指数进行处理,使处理后的图像中大多数点位于平滑区域的同时,谱的相对强度没有变化,从而取得最佳效果.实验结果表明,该方法在去除噪声的同时可很好地保留原始图像的纹理信息.     

一种基于多重分形新特征的图像分割算法

提出了一种新的基于容度的多重分形图象分析方法.在特征提取方面利用了基于Choquet容度的不同度量标准.从不同的角度提取信息,最大限度地利用了图像中的纹理信息,能将不同类型的纹理有效地区分开.同时结合模糊神经网络提出了一种基于自适应模糊聚类方法的图像纹理分类新算法,不仅克服了经典算法的不足,而且能自动确定网络结构.通过对实际图像的分割试验,证实了该方法的有效性.     

Generation of realistic 3D concrete aggregate microstructures using multiscale multifractal evolutionary stochastic manifold and operator-split-genetic algorithm

Concrete aggregates have a random and complex microstructure. This study presents a computational framework and methodology for realistic representation, simulation, and optimization of stochastic 3D aggregate microstructures. Central to the proposed methodology is the representation of aggregate microstructures as multiscale multifractal evolutionary stochastic manifolds that evolve over time in the topological space. In addition to the manifold representation scheme, a coupled-operator-split-genetic algorithm is also developed for the simulation and optimization of aggregate microstructures. The proposed scheme is particularly attractive due to its simplicity and ability to capture the complex morphological, topographical, and evolutionary characteristics of aggregate microstructures. More than a new method, this study introduces a novel concept of multiscale multifractal evolutionary hypersurface for the simulation and optimization of aggregate microstructures. The applicability and capability of the proposed approach may open up new ways to better understand, characterize, simulate, and capture many complex micromechanical behaviors of cementitious materials.     

核域多重分形谱感知的流识别与分类

关于流识别与分类,目前主流的技术是基于统计学方法,核心环节是提取有效的特征属性集。这种方法的假设条件是,特征互不相关,数据也互不相关。正因为这种假设的不合理性,使得分类效果和识别性能有限。虽然已经有很多研究在集中解决特征相关性问题,但数据相关性却难以突破。因此引入以数据相关性为核心的多重分形理论,在此基础上形成流的分形估计谱,并用相关理论检验其正确性,然后在定义的核域内基于灰色关联度进行谱分析,继而脱离特征提取过程实现流的分类识别,最后通过系列实验体现该方法在未知流分类、在线分类等方面的实际效果。